Abstract
We discuss whether position measurements in quantum mechanics can be contradictory with Bohmian trajectories, leading to what has been called “surrealistic trajectories” in the literature. Previous work has considered that a single Bohmian position can be ascribed to the pointer. Nevertheless, a correct treatment of a macroscopic pointer requires that many particle positions should be included in the dynamics of the system, and that statistical averages should be made over their random initial values. Using numerical as well as analytical calculations, we show that these surrealistic trajectories exist only if the pointer contains a small number of particles; they completely disappear with macroscopic pointers. With microscopic pointers, non-local effects of quantum entanglement can indeed take place and introduce unexpected trajectories, as in Bell experiments; moreover, the initial values of the Bohmian positions associated with the measurement apparatus may influence the trajectory of the test particle, and determine the result of measurement. Nevertheless, a detailed observation of the trajectories of the particles of the pointer reveals the nature of the trajectory of the test particle; nothing looks surrealistic if all trajectories are properly interpreted.
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L. de Broglie, La mécanique ondulatoire et la structure atomique de la matière et du rayonnement, J. Phys. Radium 8, 225 (1927)
L. de Broglie, Interpretation of quantum mechanics by the double solution theory, Ann. Fond. Louis Broglie 12, 1 (1987)
L. de Broglie,Tentative d’Interprétation causale et non-linéaire de la Mécanique Ondulatoire (Gauthier-Villars, Paris, 1956)
D. Bohm, A suggested interpretation of the quantum theory in terms of hidden variables, Phys. Rev. 85, 166 (1952)
D. Bohm, A suggested interpretation of the quantum theory in terms of hidden variables, Phys. Rev. 85, 180 (1952)
P.R. Holland,The Quantum Theory of Motion, (Cambridge University Press, Cambridge, 1993)
X. Oriols, J. Mompart, Overview of Bohmian mechanics, inApplied Bohmian mechanics: from nanoscale systems to cosmology, (Editorial Pan Stanford Publishing Pte. Ltd., 2012), Chap. 1, pp. 15–147; https://doi.org/arXiv:1206.1084v2[quant-ph]
J. Bricmont,Making Sense of Quantum Mechanics, (Springer, Berlin, 2016)
R.B. Griffiths, Bohmian mechanics and consistent histories, Phys. Lett. A 261, 227 (1999)
B.G. Englert, M.O. Scully, G. Süssmann, H. Walther, Surrealistic Bohm trajectories, Z. Naturforschung, 47a, 1175 (1992)
D. Dürr, W. Fusseder, S. Goldstein, N. Zanghi, Comments on surrealistic Bohm trajectories, Z. Naturforschung, 48a, 1261 (1993)
C. Dewdney, L. Hardy, E.J. Squires, How late measurements of quantum trajectories can fool a detector, Phys. Lett. A 184, 61 (1993)
Y. Aharonov, L. Vaidman, About position measurements which do not show the Bohmian particle position, inBohmian Mechanics and Quantum Theory: An Appraisal, edited by J.T. Cushing et al. (Kluwer, 1996), p. 141
M.O. Scully, Do Bohm trajectories always provide a trustworthy physical picture of particle motion? Phys. Scripta T 76, 41 (1998)
Y. Aharonov, B.-G. Englert, M.O. Scully, Protective measurements and Bohm trajectories, Phys. Lett. A 263, 137 (1999)
B.J. Hiley, Welcher Weg experiments from the Bohm perspective, Quantum theory: reconsiderations of foundations; Växjö conbference, AIP Conf. Proc. 810, 154 (2006)
H.M. Wiseman, Grounding Bohmian mechanics in weak values and bayesianism, New J. Phys. 9, 165 (2007)
D. Dürr, S. Goldstein, N. Zanghi, Comments on surrealistic Bohm trajectories, J. Stat. Phys. 134, 1023 (2009)
W.P. Schleich, M. Freyberger, M.S. Zubairy, Reconstruction of Bohm trajectories and wave functions from interferometric measurements, Phys. Rev. A 87, 014102 (2013)
N. Gisin, Why Bohmian mechanics? https://doi.org/arXiv:1509.00767[quant-ph] (2015)
S. Kocsis, B. Braverman, S. Ravets, M.J. Stevens, R.P. Mirin, L.K. Shalm, A.M. Steinberg, Observing the average trajectories of single photons in a two slit interferometer, Science 332, 1170 (2011)
B. Braveman, C. Simon, Proposal to observe the nonlocality of Bohmian trajectories with entangled photons, Phys. Rev. Lett. 110, 060406 (2013)
D.H. Mahler, L. Rozema, K. Fisher, L. Vermeyden, K.J. Resch, H.W. Wiseman, A. Steinberg, Experimental nonlocal and surreal Bohmian trajectories, Sci. Adv. 2, e1501466 (2016)
F. Laloë,Comprenons-nous Vraiment la Mécanique Quantique? 2nd edn. (EDP Sciences, 2018); see in particular Appendix I
G. Naaman-Marom, N. Erez, L. Vaidman, Position measurements in the de Broglie–Bohm interpretation of quantum mechanics, Ann. Phys. 327, 2522 (2012)
Wolfram Research Inc., Mathematica, Version 11.1 (Champaign, IL, 2017)
Y. Xiao, Y. Kedem, J.-S. Xu, C.-F. Li, G.-C. Guo, Experimental nonlocal steering of Bohmian trajectories, Opt. Express 25, 14643 (2017)
J.S. Bell, de Broglie-Bohm, delayed-choice double-slit experiment, and density matrix, Int. J. Quantum Chem. 14, 155 (1980)
M. Toroš, S. Donaldi, A. Bassi, Bohmian mechanics, collapse models and the emergence of classicality, J. Phys. A 49, 355302 (2016)
M. Correggi, G. Morchio, Quantum mechanics and stochastic mechanics for compatible observables at different times, Ann. Phys. 296, 371 (2002)
A. Neumaier, Bohmian mechanics contradicts quantum mechanics, https://doi.org/arXiv:quant-ph/0001011 (2000)
X. Oriols, A. Benseny, Conditions for the classicality of the center of mass of manyparticle quantum states, New J. Phys. 19, 063031 (2017)
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Tastevin, G., Laloë, F. Surrealistic Bohmian trajectories do not occur with macroscopic pointers. Eur. Phys. J. D 72, 183 (2018). https://doi.org/10.1140/epjd/e2018-90129-4
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DOI: https://doi.org/10.1140/epjd/e2018-90129-4